Let F be a finite field of characteristic p. The structures of the unit groups of group algebras over F for the three groups D24, S4 and SL(2, ℤ3) of order 24 are completely described in numerous works. We present the unit groups of group algebras over F for the remaining groups of order 24, namely, C24, C12 × C2, \({C}_{2}^{3}\) × C3, C3 ⋊ C8, C3 ⋊ Q8, D6 × C4, C6 ⋊ C4, C3 ⋊ D8, C3 × D8, C3 × Q8, A4 × C2, and D12 × C2.
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References
A. A. Bovdi and J. Kurdics, “Lie properties of the group algebra and the nilpotency class of the group of units,” J. Algebra, 212, No. 1, 28–64 (1999).
R. A. Ferraz, “Simple components of the center of FG/J(FG),” Comm. Algebra, 36, No. 9, 3191–3199 (2008).
The GAP Groups. GAP-Groups, Algorithms and Programming, Version 4.7.8 (2015); http://www.gap-system.org.
T. Hurley, “Group rings for communications,” Int. J. Group Theory, 4, 1–23 (2015).
M. Khan, R. K. Sharma, and J. B. Srivastava, “The unit group of FS4,” Acta Math. Hungar., 118, No. 1-2, 105–113 (2008).
S. Maheshwari, “The unit group of group algebras FqSL(2, ℤ3),” J. Algebra Comb. Discrete Struct. Appl., 3, No. 4, 1–6 (2016).
S. Maheshwari and R. K. Sharma, “A note on units in FqSL(2, ℤ3),” Ukr. Math. Zh., 73, No. 8, 1147–1152 (2021); English translation: Ukr. Math. J., 73, No. 8, 1331–1337 (2022); https://doi.org/10.1007/s11253-022-01994-7.
C. P. Milies and S. K. Sehgal, An introduction to Group Rings. Algebra and Applications, Vol. 1, Kluwer Academic Publishers, Dordrecht (2002).
F. Monaghan, “Units of some group algebras of non-Abelian groups of order 24 over any finite field of characteristic 3,” Int. Electron. J. Algebra, 12, 133–161 (2012).
V. S. Pless and W. C. Huffman, Handbook of Coding Theory, Elsevier, New York (1998).
R. E. Sabin and S. J. Lomonaco, “Metacyclic error-correcting codes,” Appl. Algebra Eng. Comm. Comput., 6, No. 3, 191–210 (1995).
M. Sahai and S. F. Ansari, “Unit groups of group algebras of certain dihedral groups-II,” Asian-Europ. J. Math., 12, No. 4 (2019).
M. Sahai and S. F. Ansari, “Unit groups of finite group algebras of Abelian groups of order at most 16,” Asian-Europ. J. Math., 14, No. 3 (2021).
M. Sahai and S. F. Ansari, “Unit groups of group algebras of groups of order 18,” Comm. Algebra, 49, No. 8, 3273–3282 (2021).
G. Tang and G. Yanyan, “The unit group of FG of group with order 12,” Int. J. Pure Appl. Math., 73, No. 2, 143–158 (2011).
G. Tang, Y.Wei, and Y. Li, “Unit groups of group algebras of some small groups,” Czechoslovak Math. J., 64, No. 1, 149–157 (2014).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 2, pp. 215–229, February, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i2.6680.
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Sahai, M., Ansari, S.F. Group of Units of Finite Group Algebras for Groups of Order 24. Ukr Math J 75, 244–261 (2023). https://doi.org/10.1007/s11253-023-02197-4
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DOI: https://doi.org/10.1007/s11253-023-02197-4